Volume 5, page 335, question 35 otherwise, question, interest, affect

yuoska

Volume 5, page 335, question 35
According to the answer:
“The value of a callable bond equals the value of an otherwise identical non-callable bond minus the value of the call. A rise in interest rates will reduce the value of the non-callable portion and thus reduce the value of the callable bond.”
Does not the rise in interest rates also affect the value of the call?
If we use a new interest rate tree with higher rates to value the call, we would get a lower call value.
The lower interest rates will cause the no callable to be worth less at any point in the tree, and thus less likely to be called, and thus call worth less…?

SFoyil

You shouldn’t say, “callable worth more”; you should say “callable worth less less”. The direction will still be down, necessarily. Interest rates just affect all three components.
I was trying to get at it before when I said the value of the call ranges from near 0, to the value of the non-callable bond:
Scen 1: Interest rates go way down and approach zero. The bond is called under all conditions, and there is little to no value in a callable bond, since the option is worth near the bond price.
Scen 2: Interest raise rise very, very high. The option has little chance to be exercised, and has no value; in this situation the value of the callable bond is near the same as the non-callable bond. BUT! This value is low, since a high interest rate reduces the value of the bond (PV of cash flows) – everything is going toward zero here.
The true statement in the problem says “interest rates are rising in a low-interest environment, the value of the callable bonds should decrease.” Value of everything is going to decrease, and you’re correct that the degree of the decrease will depend on the strike amount; however that doesn’t change the fact that the callable bond will decrease, too.

TheMBAGlover

@SeesFA,
I agree that the interest rate rise will affect both bonds.
But in terms of the call option, thinking of it as a stand alone option. Should not the rise in the rates cause the value of the call option to fall, since at each node the bond will be worth less, and thus less value for the call at each node…
and thus, if what i am saying about the price of call being affected by interest rates moving up, the effect on the callable bond becomes uncertain…
on the one hand the non-callable portion of it is going down..
but the call is also going down, which would make the callable worth more….

prashantsahni

Sure, you’re correct.
Bond_call = Bond_noncall - call_value
= call_value = Bond_noncall - Bond_call
clearly an interest rate rise will affect both bond forms. Depending on how close to strike we are, the value of the call will range anywhere to near zero, to the value of the non-callable bond.